Here is a dev board that lets you try internet connected projects easily. The SparkFun ESP8266 Thing has a microcontroller that can be programmed to control LED lights, monitor sensors, and control appliances. You can develop firmware for it in Arduino.
The ESP8266 Thing Development Board simply lets you connect your devices to the Internet. As you can see in the above video, it can be used to build an internet-connected flamethrower or other fun gadgets. Costs under $16 at this time.